Medvedev cruised to a 6-2, 6-4 win, hitting just five unforced errors to the Canadian's 20.
"Today was my best match of the week, but I have to build on this," said world number 11 Medvedev.
Medvedev next faces Grigor Dimitrov after the Bulgarian saved two match points to down Alex de Minaur 6-3, 3-6, 7-6 (8/6) in his quarter-final.
World number 14 Jannik Sinner, who shocked top seed Stefanos Tsitsipas in straight sets on Thursday, made the last-four by seeing off three-time major winner Stan Wawrinka 6-1, 6-3.
The 72-minute victory extended Sinner's winning streak to six matches after he also collected the Montpellier title last weekend.
"I just try to play every match with a high intensity, try to play my game, try to adapt myself," said Italy's Sinner.
"The first round match here was very important for me, then I try to keep going, to get more rhythm. Today I think it was also a good match. It's never easy playing against him, so I'm very happy."
Sinner will next face Dutch wild card Tallon Griekspoor who downed compatriot and world ranked 160 Gijs Brouwer 6-4, 6-4.
